S4:{5,4}

Statistics

genus c	4, orientable
Schläfli formula c	{5,4}
V / F / E c	30 / 24 / 60
notes
vertex, face multiplicity c	1, 1
Petrie polygons holes 2nd-order Petrie polygons	20, each with 6 edges 30, each with 4 edges 20, each with 6 edges
antipodal sets	15 of ( 2v ), 12 of ( 2f ), 30 of ( 2e )
rotational symmetry group	S5, with 120 elements
full symmetry group	240 elements.
its presentation c	< r, s, t | t2, s4, (sr)2, (st)2, (rt)2, r‑5, (sr‑2sr‑1)2 >
C&D number c	R4.2′
The statistics marked c are from the published work of Professor Marston Conder.

Relations to other Regular Maps

Its dual is S4:{4,5}.

Its Petrie dual is C12{6,4}₅.

It is a 2-fold cover of C5:{5,4}.

It can be 2-split to give R19.7′.
It can be 3-split to give R34.3′.
It can be 4-split to give R49.26′.
It can be 6-split to give R79.1′.
It can be 7-split to give R94.1′.

It is the result of rectifying S4:{5,5}.

List of regular maps in orientable genus 4.

Other Regular Maps

General Index

The image on this page is copyright © 2010 N. Wedd